Myo Min Aung Unified Theory (MUT) v7.7: The Geometric Origin of the Rydberg Constant: A Derivation from the Mass Curvature Rate fMCR (Supplementary Material to v7.0)

Myo Min Aung Unified Theory (MUT) v7.7 explores the geometric origin of the Rydberg constant within the Mass Curvature Rate framework introduced in MUT v7.0. In conventional quantum mechanics, the Rydberg constant determines the spectral structure of hydrogen and is expressed through the coupling of electron mass, electric charge, and the fine-structure constant. While this formulation is numerically accurate, it does not explain why the constant has its particular value.Within the MUT framework, the Rydberg frequency (f_Ryd = c × R_infinity) is interpreted as a harmonic of the universal Mass Curvature Rate constant f_MCR. The theory proposes a scaling identity of the form:f_Ryd = Psi × f_MCRwhere Psi is a geometric scaling factor with dimensions of linear mass density. Using the measured values of the Rydberg frequency and the Mass Curvature Rate constant, the scaling factor is obtained as Psi ≈ 1.8355 × 10^-20 kg/m.This result establishes a direct relationship between atomic spectral structure and spacetime curvature. The same constant f_MCR that connects mass and geometry at nuclear and gravitational scales also determines the fundamental frequency scale of atomic transitions.An additional observation is that the magnitude of Psi is comparable to the Planck-to-proton mass ratio (m_p / M_Planck ≈ 7.68 × 10^-20). This numerical proximity suggests that atomic stability and the extreme weakness of gravity may arise from a common curvature suppression mechanism.The framework further allows the Bohr radius and the fine-structure constant to be expressed through combinations of f_MCR, Psi, and standard physical constants, indicating that several atomic constants may emerge from the same geometric structure.If atomic constants originate from spacetime curvature dynamics, the theory predicts extremely small variations of atomic spectral constants in strong gravitational environments. Such effects are predicted to be extremely small under terrestrial conditions but may become relevant near compact astrophysical objects.By linking atomic spectral physics to the Mass Curvature Rate constant, MUT v7.7 extends the unification program of the theory from nuclear and gravitational scales to the domain of atomic structure and quantum spectra. This document serves as supplementary material to MUT v7.0 and contributes to the broader geometric interpretation of fundamental physical constants.